1. Which expressions is the prime factorization of 90

In a study of red/green color blindness, 700 men and 2850 women are randomly selected and tested. Among the men, 66 have red/gre

olga55 [171]

Answer:

$z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197$

$p_v =P(Z>15.197) \approx 0$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

Step-by-step explanation:

Data given and notation

$X_{M}=66$ represent the number of men with red/green color blindness.

$X_{W}=8$ represent the number of women with red/green color blindness.

$n_{M}=700$ sample of male slected

$n_{W}=2850$ sample of female selected

$p_{M}=\frac{66}{700}=0.0943$ represent the proportion of male with red/green color blindness.

$p_{W}=\frac{8}{2850}=0.00281$ represent the proportion of female with red/green color blindness.

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion of men with red/green color blindness. is higher than the proportionof women with red/green color blindness. , the system of hypothesis would be:

Null hypothesis: $p_{M} \leq p_{W}$

Alternative hypothesis: $p_{M} > p_{W}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{66+8}{700+2850}=0.0208$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =P(Z>15.197) \approx 0$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

8 0

3 years ago

Jolanda started an art project at 9:00

Salsk061 [2.6K]

Duration, time taken, the completion time

8 0

3 years ago

Consider the following system of equations:

Delicious77 [7]

Answer:

The system has infinitely solutions

Step-by-step explanation:

we have

$-\frac{1}{3}x^{2}=-\frac{5}{6}+\frac{1}{3}y^{2}$

$\frac{1}{3}x^{2}+\frac{1}{3}y^{2}=\frac{5}{6}$

Multiply by 3 both sides

$x^{2}+y^{2}=\frac{5}{2}$ ----> equation A

The equation A is a circle centered at origin with radius $r=\sqrt{5/2}\ units$

and

$5y^{2} =\frac{25}{2}-5x^{2}$

$5x^{2}+5y^{2} =\frac{25}{2}$

Divide by 5 both sides

$x^{2}+y^{2} =\frac{5}{2}$ ----> equation B

The equation B is a circle centered at origin with radius $r=\sqrt{5/2}\ units$

Equation A and Equation B are the same

Therefore

The system has infinitely solutions

7 0

3 years ago

Read 2 more answers

before tomorrow can I have a quick answer and maybe an explanation on how to answer these kinds of questions overall? need some

MA_775_DIABLO [31]

Answer:

a) maximum; the parabola opens downward

b) positive; it must lie above the x-axis

c) x = 1.5

Step-by-step explanation:

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.

The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.

__

If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.

__

The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:

x = (-2 +5)/2 = 3/2

The x-coordinate of the vertex is x = 1.5.

______

<em>Additional comment</em>

The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.

3 0

2 years ago

Describe, in words, the solution set for the following equation.<br><br> 3x+3=3+3x

juin [17]

Answer:

Infinite Answers

Step-by-step explanation:

You subtract 3x from both side which leaves you with 3=3, which leaves you to conclude there are infinite answers to this equation.

5 0

3 years ago